{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"apy"},"result":{"entity_type":"calculator","id":"apy","calculator_id":"apy","canonical_url":"https://tttkmbb.com/finance/apy","name":"APY Calculator","title":"APY Calculator – Convert APR to Annual Percentage Yield by Compounding Frequency","category":"finance","category_name":"Finance","tool_name":"convert_apr_to_apy","featured_mcp_tool":false,"description":"Converts a nominal annual rate (APR) into the effective annual yield (APY) for a given compounding frequency, and reports the periodic rate and the one-year growth of 1,000.","use_when":"You want to compare deposit accounts or loans quoted with different compounding frequencies, or need the effective annual rate for a nominal rate.","do_not_use_when":"You need a balance after several years or with deposits (use compound-interest), or the account quotes an APY already and you want the nominal rate (enter it as annual compounding).","inputs":[{"name":"apr_percent","label":"Nominal annual rate (APR)","type":"number","unit":"%","required":true,"min":0,"max":1000,"description":"Stated annual rate in percent before compounding; 5 means 5 %.","example":5},{"name":"compounding_frequency","label":"Compounding frequency","type":"enum","required":false,"default":"monthly","values":[{"value":"annually","label":"Annually (1×/year)","aliases":["yearly","annual","1"]},{"value":"semiannually","label":"Semiannually (2×/year)","aliases":["semi-annually","half-yearly","2"]},{"value":"quarterly","label":"Quarterly (4×/year)","aliases":["4"]},{"value":"monthly","label":"Monthly (12×/year)","aliases":["12"]},{"value":"weekly","label":"Weekly (52×/year)","aliases":["52"]},{"value":"daily","label":"Daily (365×/year)","aliases":["365"]}],"description":"How often interest is credited: n = 1, 2, 4, 12, 52 or 365 periods per year.","example":"monthly"}],"outputs":[{"name":"apy_percent","label":"APY (effective annual rate)","type":"number","unit":"%","decimals":4,"description":"(1 + APR/n)^n − 1, in percent."},{"name":"periodic_rate_percent","label":"Rate per period","type":"number","unit":"%","decimals":6,"description":"APR / n, the rate applied each compounding period."},{"name":"periods_per_year","label":"Periods per year","type":"integer","decimals":0,"description":"n for the chosen compounding frequency."},{"name":"apy_minus_apr_percentage_points","label":"APY − APR","type":"number","unit":"percentage points","decimals":4,"description":"Extra yield produced by compounding within the year."},{"name":"balance_of_1000_after_one_year","label":"1,000 after one year","type":"number","decimals":2,"description":"1000 × (1 + APY)."}],"input_schema":{"type":"object","properties":{"apr_percent":{"description":"Stated annual rate in percent before compounding; 5 means 5 %. Unit: %.","type":"number","minimum":0,"maximum":1000,"examples":[5],"x-unit":"%"},"compounding_frequency":{"description":"How often interest is credited: n = 1, 2, 4, 12, 52 or 365 periods per year.","type":"string","enum":["annually","semiannually","quarterly","monthly","weekly","daily"],"default":"monthly","examples":["monthly"]}},"additionalProperties":false,"required":["apr_percent"]},"output_schema":{"type":"object","properties":{"apy_percent":{"description":"(1 + APR/n)^n − 1, in percent. Unit: %.","type":"number","x-unit":"%"},"periodic_rate_percent":{"description":"APR / n, the rate applied each compounding period. Unit: %.","type":"number","x-unit":"%"},"periods_per_year":{"description":"n for the chosen compounding frequency.","type":"integer"},"apy_minus_apr_percentage_points":{"description":"Extra yield produced by compounding within the year. Unit: percentage points.","type":"number","x-unit":"percentage points"},"balance_of_1000_after_one_year":{"description":"1000 × (1 + APY).","type":"number"}}},"formula":"APY = (1 + apr_percent/100 / n)^n − 1, where n = compounding periods per year (1, 2, 4, 12, 52 or 365)","method":"This is the effective-annual-rate formula prescribed by US Regulation DD (Truth in Savings) for deposit accounts; it ignores fees and assumes the rate stays constant for a year.","sources":[{"name":"Investopedia – Annual Percentage Yield (APY): What It Is and How It Works","url":"https://www.investopedia.com/terms/a/apy.asp","type":"reference","retrieved_at":"2026-09-23"},{"name":"12 CFR Part 1030 – Truth in Savings (Regulation DD), Appendix A: APY calculation","url":"https://www.ecfr.gov/current/title-12/chapter-X/part-1030","type":"government","retrieved_at":"2026-09-23"},{"name":"Wikipedia – Effective interest rate","url":"https://en.wikipedia.org/wiki/Effective_interest_rate","type":"reference","retrieved_at":"2026-09-23"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"5 % APR compounded monthly","inputs":{"apr_percent":5,"compounding_frequency":"monthly"},"expected":{"apy_percent":5.1162,"periodic_rate_percent":0.416667,"periods_per_year":12,"apy_minus_apr_percentage_points":0.1162,"balance_of_1000_after_one_year":1051.16},"url":"https://tttkmbb.com/api/v1/calculate/apy?apr_percent=5&compounding_frequency=monthly"},{"name":"4 % APR compounded daily","inputs":{"apr_percent":4,"compounding_frequency":"daily"},"expected":{"apy_percent":4.0808,"periods_per_year":365,"balance_of_1000_after_one_year":1040.81},"url":"https://tttkmbb.com/api/v1/calculate/apy?apr_percent=4&compounding_frequency=daily"}],"faq":[{"q":"What is the difference between APR and APY?","a":"APR is the nominal rate before compounding; APY is the rate you actually earn (or pay) in a year once interest is compounded. They are equal only with annual compounding."},{"q":"How do I go from APY back to APR?","a":"APR = n × ((1 + APY)^(1/n) − 1). For 5.1162 % APY with monthly compounding that gives 5.00 % APR."}],"tags":["apy","apr to apy","effective annual rate","compounding frequency","annual percentage yield"],"related":[{"calculator_id":"compound-interest","reason":"Grow a balance at this rate over several years."},{"calculator_id":"rule-of-72","reason":"Estimate how long the rate takes to double money."}],"links":{"html":"https://tttkmbb.com/finance/apy","markdown":"https://tttkmbb.com/finance/apy.md","json":"https://tttkmbb.com/finance/apy.json","api":"https://tttkmbb.com/api/v1/calculate/apy","schema":"https://tttkmbb.com/api/v1/calculators/apy","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-23"},"timestamp":"2026-09-23T23:23:05Z"}